In this paper, we propose a fully convolutional network-based dense map from voxels to invertible pair of displacement vector fields regarding a template grid for the consistent voxel-wise correspondence. We parameterize the volumetric mapping using a convolutional network and train it in an unsupervised way by leveraging the spatial transformer to minimize the gap between the warped volumetric image and the template grid. Instead of learning the unidirectional map, we learn the nonlinear mapping functions for both forward and backward transformations. We introduce the combinational inverse constraints for the volumetric one-to-one maps, where the pairwise and triple constraints are utilized to learn the cycle-consistent correspondence maps between volumes. Experiments on both synthetic and clinically captured volumetric cone-beam CT (CBCT) images show that the proposed framework is effective and competitive against state-of-the-art deformable registration techniques.
Polynomial mapping functions
